Shortest Connectivity: An Introduction with Applications in Phylogeny

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Springer Science & Business Media, 2004. 11. 19. - 268페이지
The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology.

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TWO CLASSICAL OPTIMIZATION PROBLEMS
1
12 MINIMUM SPANNING TREES
11
GAUSS QUESTION
21
22 EXAMPLES AND EXERCISES
27
23 REFERENCES
30
24 A FIRST ANALYSIS OF STEINERS PROBLEM
31
25 STEINERS PROBLEM IN GRAPHS
46
WHAT DOES SOLUTION MEAN?
55
53 APPLICATIONS AND RELATED QUESTIONS
160
AN ANALYSIS OF STEINERS PROBLEM IN PHYLOGENETIC SPACES
171
62 MORE ABOUT TREES
174
63 CLUSTER ANALYSIS
192
64 SPANNING TREES
199
65 COUNTING THE ELEMENTS IN DISCRETE METRIC SPACES
201
66 FERMATS PROBLEM IN SEVERAL DISCRETE METRIC SPACES
206
TREE BUILDING ALGORITHMS
209

32 DOES A SOLUTION EXIST?
58
33 DOES AN ALGORITHM EXIST?
59
34 DOES AN EFFICIENT ALGORITHM EXIST?
61
35 DOES AN APPROXIMATION EXIST?
74
NETWORK DESIGN PROBLEMS
83
42 Several Variants
92
A NEW CHALLENGE THE PHYLOGENY
123
51 PHYLOGENETIC TREES
124
52 PHYLOGENETIC SPACES
131
71 TREE BUILDING METHODS AN OVERVIEW
211
72 MAXIMUM PARSIMONY METHOD
213
73 THE PERFECT PHYLOGENY PROBLEM
215
74 PAIR GROUP METHODS
217
75 STEINERIZATION
222
76 HANDLING MORE THAN ONE TREE
226
REFERENCES
231
INDEX
263
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